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Phase Portrait Methods for Verifying Fluid Dynamic Simulations

H. Bruce Stewart

出版	Brookhaven National Lab., 1989
URL	http://books.google.com.hk/books?id=x2_ijgEACAAJ&hl=&source=gbs_api

註釋

As computing resources become more powerful and accessible, engineers more frequently face the difficult and challenging engineering problem of accurately simulating nonlinear dynamic phenomena. Although mathematical models are usually available, in the form of initial value problems for differential equations, the behavior of the solutions of nonlinear models is often poorly understood. A notable example is fluid dynamics: while the Navier-Stokes equations are believed to correctly describe turbulent flow, no exact mathematical solution of these equations in the turbulent regime is known. Differential equations can of course be solved numerically, but how are we to assess numerical solutions of complex phenomena without some understanding of the mathematical problem and its solutions to guide us.